Error: random, 312 systematic

When standardizing a solution of NaOH against potassium hydrogen phthalate (KHP), a variety of systematic and random errors are possible. Identify, with justification, whether the following are systematic or random sources of error, or if they have no effect. If the error is systematic, then indicate whether the experimentally determined molarity for NaOH will be too high or too low. The standardization reaction is... 

When an analyst performs a single analysis on a sample, the difference between the experimentally determined value and the expected value is influenced by three sources of error random error, systematic errors inherent to the method, and systematic errors unique to the analyst. If enough replicate analyses are performed, a distribution of results can be plotted (Figure 14.16a). The width of this distribution is described by the standard deviation and can be used to determine the effect of random error on the analysis. The position of the distribution relative to the sample s true value, p, is determined both by systematic errors inherent to the method and those systematic errors unique to the analyst. For a single analyst there is no way to separate the total systematic error into its component parts. 

Relationship between point In a two-sample plot and the random error and systematic error due to the analyst. 

This test code specifies procedures for evaiuation of uncertainties in individuai test measurements, arising from both random errors and systematic errors, and for the propagation of random and systematic uncertainties... 

Linearity. Whether the chosen linear model is adequate can be seen from the residuals ey over the x values. In Fig. 6.8a the deviations scatter randomly around the zero fine indicating that the model is suitable. On the other hand, in Fig. 6.8b it can be seen that the errors show systematic deviations and even in the given case where the deviations alternate in the real way, it is indicated that the linear model is inadequate and a nonlinear model must be chosen. The hypothesis of linearity can be tested ... 

If you answered (b), perhaps you were thinking of the spread of values obtained from replicate measurements. While these do indeed form a range, one such range will relate to only one source of uncertainty and there may be several sources of uncertainty affecting a particular measurement. The precision of a measurement is an indication of the random error associated with it. This takes no account of any systematic errors that may be connected with the measurement. It is important to realize that uncertainty covers the effects of both random error and systematic error and, moreover, takes into account multiple sources of these effects where they are known to exist and are considered significant. 

Measurements can contain any of several types of errors (1) small random errors, (2) systematic biases and drift, or (3) gross errors. Small random errors are zero-mean and are often assumed to be normally distributed (Gaussian). Systematic biases occur when measurement devices provide consistently erroneous values, either high or low. In this case, the expected value of e is not zero. Bias may arise from sources such as incorrect calibration of the measurement device, sensor degradation, damage to the electronics, and so on. The third type of measurement... 

Because measurements always contain some type of error, it is necessary to correct their values to know objectively the operating state of the process. Two types of errors can be identified in plant data random and systematic errors. Random errors are small errors due to the normal fluctuation of the process or to the random variation inherent in instrument operation. Systematic errors are larger errors due to incorrect calibration or malfunction of the instruments, process leaks, etc. The systematic errors, also called gross errors, occur occasionally, that is, their number is small when compared to the total number of instruments in a chemical plant. 

Potential errors in epidemiological studies are divided into random error and systematic error (bias) (WHO 2002). 

SYSTEMATIC ERRORS RANDOM ERROR STATISTICS (A Primer)... 

Define Quality Control, Quality Assurance, sample, analyte, validation study, accuracy, precision, bias, calibration, calibration curve, systematic error, determinate error, random error, indeterminate error, and outlier. 

Both random errors and systematic errors in the measurements of x, y, or z lead to error in the determination of u in Eq. (8.1). Since systematic errors shift measurement in a single direction, we use du to treat systematic errors. In contrast, since random errors can be both positive and negative, we use (du) to treat random errors. 

As already mentioned in the introduction, ruggedness is a part of the precision evaluation. Precision is a measure for random errors. Random errors cause imprecise measurements. Another kind of errors that can occur are systematic errors. They cause inaccurate results and are measured in terms of bias. The total error is defined as the sum of the systematic and random errors. 

There are three types of data error random error in the reference laboratory values, random error in the optical data, and systematic error in the relationship between the two. The proper approach to data error depends on whether the affected variables are reference values or spectroscopic data. Calibrations are usually performed empirically and are problem specific. In this situation, the question of data error becomes an important issue. However, it is difficult to decide if the spectroscopic error is greater than the reference laboratory method error, or vice versa. The noise of current NIR instrumentation is usually lower than almost anything else in the calibration. The total error of spectroscopic data includes... 

The more traditional distinction of error components is between random errors and systematic errors. In this classical approach, random errors are generally referred to as precision (repeatability, intermediate precision, and reproducibility), while systematic errors are typically attributed to the uncertainty on the bias estimate and... 

Round robin experiment Different people in several laboratories analyze identical samples by the same or different methods Disagreement beyond the estimated random error is systematic error. 

By far, most propagation of uncertainty computations that you will encounter deal with random error, not systematic error. Our goal is always to eliminate systematic error. 

In general, results from investigations based on measurements may be falsified by three principal types of errors gross, systematic, and random errors. In most cases gross errors are easily detected and avoidable. Systematic errors (so-called determinate errors) affect the accuracy and therefore the proximity of an empirical (experimental) result to the true result, which difference is called bias. Random errors (so-called indeterminate errors) influence the precision of analytical results. Sometimes precision is used synonymously with reproducibility and repeatability. Note that these are different measures of precision, which, in turn, is not related to the true value. 

This is the common form of the F-ratio because reproducibility is usually (much) greater than repeatability. Following the conventions of analysis of variance, which assume that repeatability is influenced by random errors whereas systematic errors might influence reproducibility and therefore yield larger values of s%prod, we have to use one-sided critical values F (feprodi frepeat-, < = 1 - ) In this case we are allowed to assume that variation of the reproducibility (over all laboratories) is random in nature. 

There are several other factors that are important when it comes to the selection of equipment in a measurement process. These parameters are items 7 to 13 in Table 1.2. They may be more relevant in sample preparation than in analysis. As mentioned before, very often the bottleneck is the sample preparation rather than the analysis. The former tends to be slower consequently, both measurement speed and sample throughput are determined by the discrete steps within the sample preparation. Modern analytical instruments tend to have a high degree of automation in terms of autoinjectors, autosamplers, and automated control/data acquisition. On the other hand, many sample preparation methods continue to be labor-intensive, requiring manual intervention. This prolongs analysis time and introduces random/systematic errors. 

Analytical results are subject to two types of errors, namely, systematic and random. Both will influence the accuracy of a test result. Accuracy has been... 

There is an important reason why excessive efforts should not be made to reduce the magnitude of random errors by making a very large number of measurements of the same quantity. This reason is that measurements are also subject to other kinds of error, chiefly systematic errors, the magnitude of which can all too easily exceed that of the random errors. A systematic error is one that cannot be reduced or eliminated by any number of repetitions of a measurement because it is inherent in the method, the instrumentation, or occasionally the interpretation of data. While the precision of a result, as already stated, is an expression of uncertainty due to random error, the accuracy of a result is an expression of overall uncertainty including that due to systematic error. Accuracy is very much more difficult to assess than precision. 

The proper implementation of calibration is to a large extent determined by careful and correct preparation of calibration solutions and samples for measurements. This is especially important in trace analysis because even the smallest errors, random or systematic, at the laboratory stage of the calibration procedure can significantly influence the precision and accuracy of the obtained results. 

The typical approach for the study of errors is to classify them as systematic (or determinate) or random. Systematic errors are generated by a specific cause, and it is assumed that by removing the cause, the systematic error is also eliminated. 

The uncertainty concept is directed toward the end user (clinician) of the result, who is concerned about the total error possible, and who is not particularly interested in the question whether the errors are systematic or random. In the outiine of the uncertainty concept it is assumed that any known systematic error components of a measurement method have been corrected, and the specified uncertainty includes the uncertainty associated with correction of the systematic error(s). Although this appears logical, a problem may be that some routine methods have systematic errors dependent on the patient category from which the sample originates. For example, kinetic Jaffe methods for creatinine are subject to positive interference by alpha-keto compounds and to negative interference by bilirubin and its metabolites, which means that the direction of systematic error will be patient dependent and not generally predictable. 

Figure 19-10 Power functions for l2s control rule. A, Random error. B, Systematic error. (From Westgard JO, Groth T. Power functions for statistical control rules. Clin Chem 1979 25 863-9.)...

The objective of any review of experimental values is to evaluate the accuracy and precision of the results. The description of a procedure for the selection of the evaluated values (EvV) of electron affinities is one of the objectives of this book. The most recent precise values are taken as the EvV. However, this is not always valid. It is better to obtain estimates of the bias and random errors in the values and to compare their accuracy and precision. The reported values of a property are collected and examined in terms of the random errors. If the values agree within the error, the weighted average value is the most appropriate value. If the values do not agree within the random errors, then systematic errors must be investigated. In order to evaluate bias errors, at least two different procedures for measuring the same quantity must be available. 

When a sample is repeatedly analyzed in the laboratory using the same measuring method, results are collected that deviate from each other to some extent. The deviations, representing a scatter of individual values around a mean value, are denoted as statistical or random errors, a measure of which is the precision. Deviations from the true content of a sample are caused by systematic errors. An analytical method only provides true values if it is free of systematic errors. Random errors make an analytical result less precise while systematic errors give incorrect values. Hence, precision of a measuring method has to be considered separately. Statements relative to the accuracy are only feasible if the true value is known. 

There will always be two different kind of contributions to the error term systematic and random enors. 

No fitting technique can be expected to replace completely the judgment of the experimentalist in distinguishing random errors from systematic errors or model deficiencies. 

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